Calculus Word Problem

[crabpot]

I've having a difficult time setting up the following calculus word problem:

A fruit grower knows from previous experience and careful data analysis that if the fruit on a specific kind of tree is harvested at this time of year, each tree will yield, on average, 133 pounds, and will sell for $0.7 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 5 pounds, while the price per pound will decrease by $0.02.

Find and give a quadratic function for the Revenue of a typical tree in the form ax^2+bx+c.

Any help is greatly appreciated!

 

[Deleted member 4993]

I've having a difficult time setting up the following calculus word problem:

A fruit grower knows from previous experience and careful data analysis that if the fruit on a specific kind of tree is harvested at this time of year, each tree will yield, on average, 133 pounds, and will sell for $0.7 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 5 pounds, while the price per pound will decrease by $0.02.

Find and give a quadratic function for the Revenue of a typical tree in the form ax^2+bx+c.

Any help is greatly appreciated!

Start with defining your variables - and show us how far you advance.

 

[crabpot]

I've having a difficult time setting up the following calculus word problem:

A fruit grower knows from previous experience and careful data analysis that if the fruit on a specific kind of tree is harvested at this time of year, each tree will yield, on average, 133 pounds, and will sell for $0.7 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 5 pounds, while the price per pound will decrease by $0.02.

Find and give a quadratic function for the Revenue of a typical tree in the form ax^2+bx+c.

Any help is greatly appreciated!

Start with defining your variables - and show us how far you advance.

I know that each tree will initially yield $93.1 (.70 x 133 pounds).

For each additional week, we will gain 5lbs in yield and decrease .02 cents per pound. This is where I get stuck.

 

[crabpot]

Do I then set it up as (.02x - .70)(5x + 133)? And foil from there?

 

[Deleted member 4993]

Do I then set it up as (.02x - .70)(5x + 133)? And foil from there?

What is 'X'?

First define your 'X'...

 

[crabpot]

Do I then set it up as (.02x - .70)(5x + 133)? And foil from there?

What is 'X'?

First define your 'X'...

X = number of weeks delayed

 

[BigGlenntheHeavy]

One way, use a chart, to wit:


Week Lbs/tree * Price/lbs. = Total Value

1 [133+(0)(5)] * [.7-(0)(.02)] = $93.10

2 [133+(1)(5)] * [.7-(1)(.02)] = $93.84

3 [133+(2)(5)] * [.7-(2)(.02)] = $94.38

. . * . = .

. . * . = .

x [133+(x-1)(5)] * [.7-(x-1)(.02)] = -.1x^(2)+1.04x+92.16


Hence, W(x) = -.1x^(2)+1.04x+92.16

 

[crabpot]

I figured it out, thanks so much for the assistance.

 

[Deleted member 4993]

I've having a difficult time setting up the following calculus word problem:

A fruit grower knows from previous experience and careful data analysis that if the fruit on a specific kind of tree is harvested at this time of year, each tree will yield, on average, 133 pounds, and will sell for $0.7 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 5 pounds, while the price per pound will decrease by $0.02.

Find and give a quadratic function for the Revenue of a typical tree in the form ax^2+bx+c.

Any help is greatly appreciated!

Revenue = (mass of product) * (price/unit mass)

If we define

x = number of weeks delayed

mass of product after "x" weeks of delay = 133 + 5*x

Price of product after "x" weeks of delay = 0.7 - 0.02*x

Revenue after "x" weeks of delay = (133 + 5*x) * (0.7 - 0.02*x) = -(5 * 0.02)x[sup:3rz4he9b]2[/sup:3rz4he9b] + x* (5 * 0.7 - 133 * 0.02) + (133 * 0.7) = -0.1 * x[sup:3rz4he9b]2[/sup:3rz4he9b] + 0.84 x + 93.10

 

[BigGlenntheHeavy]

\(\displaystyle The \ correct \ equation \ for \ the \ above \ problem \ is: \ W(x) \ = \ -.1x^{2}+1.04x+92.16, \ period.\)

\(\displaystyle Week \ one \ = \ 133 \ X \ .7 \ = \ \$93.10\)

\(\displaystyle W(1) \ = \ -.1+1.04+92.16 \ = \ \$93.10\)

\(\displaystyle Week \ three \ = \ 143 \ X \ (.7-(2)(.02)) \ = \ \$94.38\)

\(\displaystyle W(3) \ = \ -.1(9)+1.04(3)+92.16 \ = \ \$94.38\)

\(\displaystyle Week \ seven \ = \ 163 \ X \ (.7-6(.02)) \ = \ \$94.54\)

\(\displaystyle W(7) \ = \ -.1(49)+1.04(7)+92.16 \ = \ \$94.54\)

\(\displaystyle Why \ you \ are \ trying \ to \ obfuscate \ the \ problem \ "weeks \ of \ delay" \ is \ unclear \ to \ me.\)

 

[Deleted member 4993]

\(\displaystyle The \ correct \ equation \ for \ the \ above \ problem \ is: \ W(x) \ = \ -.1x^{2}+1.04x+92.16, \ period.\)

\(\displaystyle Why \ you \ are \ trying \ to \ obfuscate \ the \ problem \ "weeks \ of \ delay" \ is \ unclear \ to \ me.\)

Because that is the way student EXPLICITLY defined his/her "x"

X = number of weeks delayed